McHuron was one of three women being transported to Ophiucus III by Harcourt Fenton Mudd, as a settler's wife in 2266. Originally from the farm planet Bootes III, she had no marriage prospects, as the farms were tended by automated machinery and her brothers.
She was introduced to the Venus drug by Mudd, using it to enhance her physical attributes and allure. She was brought to the USS Enterprise after Stella, a stolen Class J cargo ship Mudd had been using, was destroyed in an asteroid belt.
McHuron's conscience worked against Mudd's plans – when he assigned her to seduce Captain Kirk, she could not carry out that plan. She also viewed the Venus drug as a trick and Harry Mudd as a con man. Worse than that, she was actually attracted to Kirk.
Mudd's scheming ultimately brought her to the surface of Rigel XII, a planet occupied by only three lithium miners. There she met Ben Childress, the chief miner. Mudd arranged for Eve and the other women to be left on the planet in exchange for lithium crystals to power the Enterprise. Eve was unhappy with the falsities and manipulations both Mudd's scheming and the Venus drug produced, and had ambivalence toward marrying one of the miners. She consequently fled Childress' home into a magnetic storm on the planet's surface. Despite the risks, both Childress and Kirk went after her. Childress eventually found her and returned to his home with her.
She and Childress sparred verbally, with tensions cuminating when the Venus drug wore off, leaving her far less appealing, and Childress angry at Mudd's deception regarding the women's beauty. After taking a dose of the drug that turned out to be a placebo and becoming beautiful again despite that, she realized that self-confidence had as much to do with appeal as the Venus drug did. Childress asked her to remain, "at least for the day," so they could talk. (TOS: "Mudd's Women")